I used to have a "special" Turkish passport, as a dependent of my father who works at the government. I have a valid USA B1/B2 visa on there. I obtained a new passport after I got a job, as my dependent status is dropped after employment.
The following website says
No. If your visa is still valid you can travel to the United States with your two passports, as long as the visa is valid, not damaged, and is the appropriate type of visa required for your principal purpose of travel. (Example: tourist visa, when your principal purpose of travel is tourism). Both passports (the valid and the expired one with the visa) should be from the same country and type (Example: both Uruguayan regular passports, both official passports, etc.). When you arrive at the U.S. port-of-entry (POE, generally an airport or land border) the Customs and Border Protection Immigration Officer will check your visa in the old passport and if s/he decides to admit you into the United States they will stamp your new passport with an admission stamp along with the annotation "VIOPP" (visa in other passport). Do not try to remove the visa from your old passport and stick it into the new valid passport. If you do so, your visa will no longer be valid.
Special passport is unique to Turkey. It is given to government officials for their personal trips, so it is not a service passport in any sense. All of my trips are touristic.
Do I need to get a new visa?